Optical methods for measuring samples are generally known, in particular, for semiconductor fabrication involving the formation of a stack of thin film layers on a semiconductor substrate. Such methods are considered essential for the efficient operation of modern fabrication facilities. Optical methods are desirable because they are non-destructive and the resultant optical data can be used to derive information regarding layer parameters, such as thickness, refractive index, extinction coefficient, dispersion and scattering, for multiple layers of a thin film stack.
One preferred approach includes the use of the OPTIPROBE detector manufactured and sold by Therma-Wave, Inc. of Fremont, Calif., assignee herein, and described in part in one or more of the following U.S. Pat. Nos. 4,999,014; 5,042,951; 5,181,080; 5,412,473; and PCT publication WO 99/02970, each of which is incorporated herein by reference in its entirety.
Conventional optical processing technology typically relies upon using a non-linear least squares algorithm to fit the measured data to a set of data points with a solution representing specific parameters of a thin film stack.
Improvements in optical technologies can provide an ever-increasing number of measured data points, which in turn provide the opportunity for deriving layer parameters on more complicated film stacks. However, this opportunity also presents a more complex optimization problem for developing solutions based on the observed data, and conventional processing techniques (such as least squares algorithms) are inadequate to handle the increased complexity.
Genetic Algorithms (GA's) have been applied to the problem of adaptive function optimization. A basic theoretical framework for GA's is described in Holland, Adaptation in Natural and Artificial Systems (1975). The terminology used by Holland is borrowed from genetics. Thus, in the computer analog, a GA is a method for defining a “population” of solutions to a selected problem, then evolving new populations by using probabilistic genetic operations to act on “individual” members of the population, i.e. individual solutions. Each individual in the population has a plurality of “genes,” which are each representative of some real parameter of interest. For example, if there are x data parameters of interest, each individual would have x genes, and populations of individuals having x genes would be propagated by a GA.
The use of GA's for function optimization is generally described in U.S. Pat. No. 5,222,192 and U.S. Pat. No. 5,255,345, both to Schaefer. Further, U.S. Pat. No. 5,394,509 to Winston generally describes the application of GA's to search for improved results from a manufacturing process. Also, there has recently been much interest in the use of GA's in the design of various types of optical filters. See Eisenhammer, et al., Optimization of Interference Filters with Genetic Algorithms Applied to Silver-Based Heat Mirrors, Applied Optics, Vol. 32 at pp. 6310–15 (1993); and Bäck & Schütz, Evolution Strategies for Mixed-Integer Optimization of Optical Multilayer Systems, Proceedings of the Fourth Annual Conference on Evolutionary Programming at pp. 33–51 (1995).
More recently, GA's have been applied to the problem of evaluating thin films on semiconductor wafers. U.S. Pat. No. 5,864,633, hereby incorporated by reference in its entirety, describes the application of GA's to the problem of evaluating the characteristics of thin film layers with an optical inspection device. The present invention is directed to an improvement on the method disclosed in U.S. Pat. No. 5,864,633 involving a multidomain optimization technique.